Subject: new Hopf listings
From: Mark Hovey
Date: 06 Oct 2006 09:12:13 -0400
I took a month off; sorry about the delay.
There are 9 new papers this time, from Bergner,
Chebolu-Christensen-Minac, DavisDaniel, Dugger-Isaksen, Fausk (2),
GrayB, Hovey-Lockridge-Puninski, and Wuethrich.
Mark Hovey
New papers appearing on hopf between 8/4/06 and 10/6/06
1.
http://hopf.math.purdue.edu/cgi-bin/generate?/Bergner/ReedyFib
Title: A characterization of fibrant Segal categories
Author: Julia E. Bergner
AMS Classification: 55U35, 18G30
Author's address: Kansas State University 138 Cardwell Hall
Manhattan, KS 66506
Abstract: In this note we prove that Reedy fibrant Segal
categories are fibrant objects in the model category structure
Secat_c. Combining this result with a previous one, we thus have
that the fibrant objects are precisely the Reedy fibrant Segal
categories. We also show that the analogous result holds for Segal
categories which are fibrant in the projective model structure on
simplicial spaces, considered as objects in the model structure
Secat_f.
2.
http://hopf.math.purdue.edu/cgi-bin/generate?/Chebolu-Christensen-Minac/ghost
[Note: I had trouble with the dvi file of this paper. I expect to have
it up by 10/7/06--Mark]
TITLE: Ghosts in modular representation theory
AUTHORS: Sunil K. Chebolu, J. Daniel Christensen, and Jan Minac
Department of Mathematics
University of Western Ontario
London, ON N6A 5B7, Canada
AMS Subject classsification: Primary 20C20, 20J06; Secondary 55P42
ABSTRACT: We study ghosts in the stable module category of a finite
group. That is, we study maps between modular representations of finite
groups which are invisible in Tate cohomology. We establish various sets
of conditions which guarantee the existence of a non-trivial ghost out
of a given representation. We then investigate the generating hypothesis
which is the statement that there are no non-trivial ghosts between
finite-dimensional representations. This is done by focusing on three
quintessential examples: the cyclic $p$-groups (finite representation
type), the Klein four group (domestic representation type), and the
quaternion groups (tame representation type). In the examples where the
generating hypothesis fails, we obtain bounds on the ghost number: the
smallest integer $l$ such that the composition of any $l$ ghosts between
finite-dimensional representations is trivial. In particular, we obtain
bounds on the ghost numbers for all $2$-groups which have a cyclic
subgroup of index $2$. Projective classes in the stable module category
play a key role in getting these bounds.
3.
http://hopf.math.purdue.edu/cgi-bin/generate?/DavisDaniel/subhg3
Title: The homotopy orbit spectrum for profinite groups
Author: Daniel G. Davis
Abstract: Let G be a profinite group. We define an S[[G]]-module to be a
G-spectrum X that satisfies certain conditions, and, given an
S[[G]]-module X, we define the homotopy orbit spectrum X_{hG}. When G is
countably based and X satisfies a certain finiteness condition, we
construct a homotopy orbit spectral sequence whose E_2-term is the
continuous homology of G with coefficients in the graded profinite
Z[[G]]-module pi_*X. Let G_n be the extended Morava stabilizer group and
let E_n be the Lubin-Tate spectrum. As an application of our theory, we
show that the function spectrum F(E_n,L_{K(n)}(S0)) is an
S[[G_n]]-module with an associated homotopy orbit spectral sequence.
4.
http://hopf.math.purdue.edu/cgi-bin/generate?/Dugger-Isaksen/etdq
Title: Etale homotopy and sums-of-squares formulas
Authors: Daniel Dugger, Daniel C. Isaksen
AMS classification number: 55P60, 15A63
Abstract:
This paper uses a relative of BP-cohomology to prove a theorem in
characteristic p algebra. Specifically, we obtain some new necessary
conditions for the existence of sums-of-squares formulas over fields of
characteristic p > 2. These conditions were previously known in
characteristic zero by results of Davis. Our proof uses a generalized
etale cohomology theory called etale BP2.
5.
http://hopf.math.purdue.edu/cgi-bin/generate?/Fausk/ArtinBrauer
Generalized Artin and Brauer induction for compact Lie groups
Halvard Fausk
Abstract:
Let $G$ be a compact Lie group. We present two induction theorems
for certain generalized $G$-equivariant cohomology theories.
The theory applies to $G$-equivariant $K$-theory $K_G$, and to
the Borel cohomology associated to any complex oriented cohomology
theory. The coefficient ring of $K_G$ is the representation ring
$R(G)$ of $G$. When $G$ is a finite group the induction theorems
for $K_G$ coincide with the classical Artin and Brauer induction
theorems for $R(G)$.
6.
http://hopf.math.purdue.edu/cgi-bin/generate?/Fausk/Gspectra-Fausk
Title: Equivariant homotopy theory for pro--spectra
Author: Halvard Fausk
Abstract. We extend the theory of equivariant orthogonal spectra from
finite groups to profinite groups, and more generally from compact Lie
groups to compact Hausdorff groups. The $G-$homotopy theory is ``pieced
together'' from the $G/U-$homotopy theories for suitable quotient groups
$G/U$ of $G$; a motivation is the way continuous group cohomology of a
profinite group is built out of the cohomology of its finite quotient
groups. In this category Postnikov towers are studied from a general
perspective. We introduce pro$-G-$spectra and construct various model
structures on them. A key property of the model structures is that
pro-spectra are weakly equivalent to their Postnikov towers. We give a
careful discussion of two version of a model structure with ``underlying
weak equivalences''. One of the versions only make sense for
pro$-$spectra. In the end we use the theory to study homotopy fixed
points of pro$-G-$spectra.
7.
http://hopf.math.purdue.edu/cgi-bin/generate?/GrayB/fiber
Filtering the fiber of the pinch map
Brayton Gray
This paper develops the similarity between the loops on an odd dimensional
sphere and the fiber F of the pinch map from an odd dimensional mod p^r
Moore space to the sphere, for p odd. In particular, a Hopf invariant map
is defined and there is an EHP sequence up to a factor which is the loops
on a bouquet of higher dimensiona Moore spaces. As a consequence we have
two technical results about the mysterious connecting map from the double
loops on the sphere to the loops on F.
8.
http://hopf.math.purdue.edu/cgi-bin/generate?/Hovey-Lockridge-Puninski/derived-gen-hyp
Title: The generating hypothesis in the derived category of a ring.
Authors: Mark Hovey, Keir Lockridge, and Gena Puninski
Abstract:
We show that a strong form (the fully faithful version) of the generating
hypothesis, introduced by Freyd in algebraic topology, holds in the
derived category of a ring R if and only if R is von Neumann regular.
This extends results of the second author. We also characterize rings for
which the original form (the faithful version) of the generating
hypothesis holds in the derived category of R. These must be close to von
Neumann regular in a precise sense, and, given any of a number of
finiteness hypotheses, must be von Neumann regular. However, we construct
an example of such a ring that is not von Neumann regular, and therefore
does not satisfy the strong form of the generating hypothesis.
9.
http://hopf.math.purdue.edu/cgi-bin/generate?/Wuethrich/thickenings_rev
Title: Infinitesimal thickenings of Morava K-theories
(revised version)
Author: Samuel Wuethrich
AMS classification number: 55P42, 55P43; 55U20, 55N22
Abstract:
This is a revised version. A few points have been clarified
and some typos have been corrected.
A. Baker has constructed certain sequences of cohomology theories
which interpolate between the Johnson-Wilson and the Morava
K-theories. We realize the representing sequences of spectra as
sequences of MU-algebras. Starting with the fact that the spectra
representing the Johnson-Wilson and the Morava K-theories admit
such structures, we construct the sequences by inductively
forming singular extensions. Our methods apply to other pairs of
MU-algebras as well.
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